paragraph40.75ex plus1ex minus.2ex-1emAlignment.
In Equation REF  we introduce the alignment operator \(\alpha _{B_{ij}}(\cdot )\) .
This is necessary because \(x_{t_j}\)  and \(x_{t_i}\)  cover different parts of the input image and thus \(Q_{t_j}\)  and the cluster assignment prediction \(Z_{t_i}^T C\)  correspond to different image areas.
To tackle this, \(\alpha (\cdot )\)  restores the spatial dimensions \(\left\lfloor {\frac{H}{P}}\right\rfloor \times \left\lfloor {\frac{W}{P}}\right\rfloor \)  and aligns the tensor using the crop intersection bounding boxes \(B_{ji}\)  and \(B_{ij}\)  respectively.
In our experiments we use RoI-Align [1]} that produces features with a fixed and compatible output size.
